Editing Meissner effect

{{Electromagnetism}}
{{Short description|Expulsion of a magnetic field from a superconductor}}
[[Image:EfektMeisnera.svg|thumb|right|Diagram of the Meissner effect. Magnetic field lines, represented as arrows, are excluded from a superconductor when it is below its critical temperature.]]

In [[condensed-matter physics]], the '''Meissner effect''' (or '''Meißner–Ochsenfeld effect''') is the expulsion of a [[magnetic field]] from a [[superconductor]] during its transition to the superconducting state when it is cooled below the critical temperature. This expulsion will repel a nearby [[magnet]].

The German physicists [[Walther Meissner|Walther Meißner]] (anglicized ''Meissner'') and [[Robert Ochsenfeld]]<ref>{{Cite news|url=https://www.britannica.com/science/Meissner-effect|title=Meissner effect {{!}} physics|work=Encyclopedia Britannica|access-date=22 April 2017|language=en}}</ref> discovered this phenomenon in 1933 by measuring the magnetic field distribution outside superconducting tin and lead samples.<ref name="meissner1">
{{Cite journal
 |last1=Meissner |first1=W.
 |last2=Ochsenfeld |first2=R.
 |year=1933
 |title=Ein neuer Effekt bei Eintritt der Supraleitfähigkeit
 |journal=[[Naturwissenschaften]]
 |volume=21 |issue=44 |pages=787–788
 |bibcode=1933NW.....21..787M
 |doi=10.1007/BF01504252
|s2cid=37842752
 }}</ref> The samples, in the presence of an applied magnetic field, were cooled below their [[Superconductivity#Superconducting phase transition|superconducting transition temperature]], whereupon the samples cancelled nearly all interior magnetic fields. They detected this effect only indirectly because the [[magnetic flux]] is conserved by a superconductor: when the interior field decreases, the exterior field increases. The experiment demonstrated for the first time that superconductors were more than just perfect [[Electrical conductor|conductors]] and provided a uniquely defining property of the superconductor state. The ability for the expulsion effect is determined by the nature of equilibrium formed by the neutralization within the [[unit cell]] of a superconductor.

A superconductor with little or no magnetic field within it is said to be in the Meissner state. The Meissner state breaks down when the applied magnetic field is too strong. Superconductors can be divided into two classes according to how this breakdown occurs. 
*In [[type-I superconductor]]s, superconductivity is abruptly destroyed when the strength of the applied field rises above a critical value ''H<sub>c</sub>''. Depending on the geometry of the sample, one may obtain an intermediate state<ref>
{{cite book
 |last1=Landau |first1=L. D.
 |last2=Lifschitz |first2=E. M.
 |year=1984
 |title=Electrodynamics of Continuous Media
 |edition=2nd
 |series=[[Course of Theoretical Physics]]
 |volume=8
 |publisher=[[Butterworth-Heinemann]]
 |isbn=0-7506-2634-8
}}</ref> consisting of a [[wikt:baroque|baroque pattern]]<ref>
{{cite journal
 |last=Callaway |first=D. J. E.
 |date=1990
 |title=On the remarkable structure of the superconducting intermediate state
 |journal=[[Nuclear Physics B]]
 |volume=344 |issue=3 |pages=627–645
 |bibcode=1990NuPhB.344..627C
 |doi=10.1016/0550-3213(90)90672-Z
}}</ref> of regions of normal material carrying a magnetic field mixed with regions of superconducting material containing no field. 
*In [[type-II superconductor]]s, raising the applied field past a critical value ''H''<sub>''c''1</sub> leads to a mixed state (also known as the vortex state) in which an increasing amount of [[magnetic flux]] penetrates the material, but there remains no resistance to the [[electric current]] as long as the current is not too large. Some type-II superconductors exhibit a small but finite resistance in the mixed state due to motion of the flux vortices induced by the Lorentz forces from the current. As the cores of the vortices are normal electrons, their motion will have dissipation. At a second critical field strength ''H''<sub>''c''2</sub>, superconductivity is destroyed. The mixed state is caused by vortices in the electronic superfluid, sometimes called [[fluxon]]s because the flux carried by these vortices is [[quantum|quantized]].

Most pure [[chemical element|elemental]] superconductors, except [[niobium]] and [[carbon nanotube]]s, are type&nbsp;I, while almost all impure and compound superconductors are type&nbsp;II.

==Explanation==

The Meissner effect was given a phenomenological explanation by the brothers [[Fritz London|Fritz]] and [[Heinz London]], who showed that the electromagnetic [[Thermodynamic free energy|free energy]] in a superconductor is minimized provided

:<math> \nabla^2\mathbf{H} = \lambda^{-2} \mathbf{H}\, </math>

where '''H''' is the magnetic field and λ is the [[London penetration depth]].

This equation, known as the [[London equation]], predicts that the magnetic field in a superconductor [[exponential decay|decays exponentially]] from whatever value it possesses at the surface. This exclusion of magnetic field is a manifestation of the [[superdiamagnetism]] emerged during the phase transition from conductor to superconductor, for example by reducing the temperature below critical temperature.

In a weak applied field (less than the critical field that breaks down the superconducting phase), a superconductor expels nearly all [[magnetic flux]] by setting up electric currents near its surface, as the magnetic field '''H''' induces [[magnetization]] '''M''' within the London penetration depth from the surface. These surface currents [[Electromagnetic shielding#Magnetic shielding|shield]] the internal bulk of the superconductor from the external applied field. As the field expulsion, or cancellation, does not change with time, the currents producing this effect (called [[persistent current]]s or screening currents) do not decay with time.

Near the surface, within the [[London penetration depth]], the magnetic field is not completely canceled. Each superconducting material has its own characteristic penetration depth.

Any perfect conductor will prevent any change to magnetic flux passing through its surface due to ordinary [[electromagnetic induction]] at zero resistance. However, the Meissner effect is distinct from this: when an ordinary conductor is cooled so that it makes the transition to a superconducting state in the presence of a constant applied magnetic field, the magnetic flux is expelled during the transition. This effect cannot be explained by infinite conductivity, but only by the London equation. The placement and subsequent levitation of a magnet above an already superconducting material does not demonstrate the Meissner effect, while an initially stationary magnet later being repelled by a superconductor as it is cooled below its critical [[temperature]] does.

The persisting currents that exist in the superconductor to expel the magnetic field is commonly misconceived as a result of [[Lenz's Law]] or [[Faraday's law of induction|Faraday's Law]]. A reason this is not the case is that no change in flux was made to induce the current. Another explanation is that since the superconductor experiences zero resistance, there cannot be an induced emf in the superconductor. The persisting current therefore is not a result of Faraday's Law.

==Perfect diamagnetism==
Superconductors in the Meissner state exhibit perfect diamagnetism, or [[superdiamagnetism]], meaning that the total magnetic field is very close to zero deep inside them (many penetration depths from the surface). This means that their volume [[magnetic susceptibility]] is <math> \chi_{v}</math> = −1. [[Diamagnetics]] are defined by the generation of a spontaneous magnetization of a material which directly opposes the direction of an applied field. However, the fundamental origins of diamagnetism in superconductors and normal materials are very different. In normal materials diamagnetism arises as a direct result of the orbital spin of electrons about the nuclei of an atom induced electromagnetically by the application of an applied field. In superconductors the illusion of perfect diamagnetism arises from persistent screening currents which flow to oppose the applied field (the Meissner effect); not solely the orbital spin.

==Consequences==
The discovery of the Meissner effect led to the [[Phenomenology (particle physics)|phenomenological]] theory of superconductivity by [[Fritz London|Fritz]] and [[Heinz London]] in 1935. This theory explained resistanceless transport and the Meissner effect, and allowed the first theoretical predictions for superconductivity to be made. However, this theory only explained experimental observations—it did not allow the microscopic origins of the superconducting properties to be identified. This was done successfully by the [[BCS theory]] in 1957, from which the penetration depth and the Meissner effect result.<ref>{{cite journal |last1=Bardeen |first1=J. |last2=Cooper |first2=L. N. |last3=Schrieffer |first3=J. R. |year=1957 |title=Theory of superconductivity |journal=[[Physical Review]] |volume=106 |issue=1175 |pages=162–164 |bibcode=1957PhRv..106..162B |doi=10.1103/physrev.106.162 |doi-access=free}}</ref> However, some physicists argue that BCS theory does not explain the Meissner effect.<ref>{{cite journal |last1=Hirsch |first1=J. E. |year=2012 |title=The origin of the Meissner effect in new and old superconductors |journal=[[Physica Scripta]] |volume=85 |issue=3 |pages=035704 |arxiv=1201.0139 |bibcode=2012PhyS...85c5704H |doi=10.1088/0031-8949/85/03/035704|s2cid=118418121 }}</ref>

<gallery widths="200px">
Image:Tin_4.2K_Electromagnet.jpg|A tin cylinder—in a Dewar flask filled with liquid helium—has been placed between the poles of an electromagnet. The magnetic field is about 8 [[millitesla]] (80 [[Gauss (unit)|G]]).
Image:Tin_80gauss_4.2K.jpg|''T'' = 4.2&nbsp;K, '''B''' = 8&nbsp;mT (80 G). Tin is in the normally conducting state. The compass needles indicate that magnetic flux permeates the cylinder.
Image:Tin_80gauss_1.6K.jpg|The cylinder has been cooled from 4.2&nbsp;K to 1.6&nbsp;K. The current in the electromagnet has been kept constant, but the tin became superconducting at about 3&nbsp;K. Magnetic flux has been expelled from the cylinder (the Meissner effect).
</gallery>

==Paradigm for the Higgs mechanism==
The Meissner superconductivity effect serves as an important paradigm for the generation mechanism of a mass ''M'' (i.e., a reciprocal ''range'', <math>\lambda_M: = h/(M c)</math> where ''h'' is the [[Planck constant]] and ''c'' is the [[speed of light]]) for a [[gauge field]]. In fact, this analogy is an [[abelian (disambiguation)#In physics|abelian]] example for the [[Higgs mechanism]],<ref>{{cite journal |last=Higgs |first=P. W. |year=1966 |title=Spontaneous symmetry breakdown without massless bosons |journal=[[Physical Review]] |volume=145 |issue=4 |pages=1156–1163 |bibcode= 1966PhRv..145.1156H|doi=10.1103/PhysRev.145.1156 |doi-access=free }}</ref> which generates the masses of the [[electroweak]] [[W and Z bosons|{{SubatomicParticle|W boson+-}} and {{SubatomicParticle|Z boson}}]] gauge particles in [[high-energy physics]]. The length <math>\lambda_M</math> is identical with the [[London penetration depth]] in the theory of [[superconductivity]].<ref>
{{Cite journal
 |last=Wilczek |first=F.
 |year=2000
 |title=The recent excitement in high-density QCD
 |journal=[[Nuclear Physics A]]
 |volume=663 |pages=257–271
 |arxiv=hep-ph/9908480
 |bibcode=2000NuPhA.663..257W
 |doi=10.1016/S0375-9474(99)00601-6
|s2cid=119354272
 }}</ref><ref>
{{cite journal
 |last=Weinberg |first=S.
 |year=1986
 |title=Superconductivity for particular theorists
 |journal=[[Progress of Theoretical Physics Supplement]]
 |volume=86 |pages=43–53
 |bibcode=1986PThPS..86...43W
 |doi=10.1143/PTPS.86.43 |doi-access=free
}}</ref>

==See also==
{{Portal|Physics|Science}}
*[[Flux pinning]]
*[[Silsbee effect]]
*[[Superfluid]]

==References==
{{Reflist}}

==Further reading==
*{{cite arXiv |last=Einstein |first=A. |author-link=Albert Einstein |year=1922 |title=Theoretical remark on the superconductivity of metals |eprint=physics/0510251}}
*{{cite book |last=London |first=F. W. |author-link=Fritz Wolfgang London |year=1961 |title=Superfluids |series=Structure of matter series |volume=1 |contribution=Macroscopic Theory of Superconductivity |edition=Revised 2nd |publisher=[[Dover Publications|Dover]] |oclc=439791906}} By the man who explained the Meissner effect. pp.&nbsp;34–37 gives a technical discussion of the Meissner effect for a superconducting sphere.
*{{cite book |last=Saslow |first=W. M. |year=2002 |title=Electricity, Magnetism, and Light |publisher=Academic |isbn=978-0-12-619455-5 }} pp.&nbsp;486–489 gives a simple mathematical discussion of the surface currents responsible for the Meissner effect, in the case of a long magnet levitated above a superconducting plane.
*{{cite book |last=Tinkham |first=M. |year=2004 |title=Introduction to Superconductivity |edition=2nd |series=Dover Books on Physics |publisher=Dover |isbn=978-0-486-43503-9}} A good technical reference.

==External links==
{{Commons|Meissner effect}}
*[https://www.feynmanlectures.caltech.edu/III_21.html#Ch21-S6 The Meissner effect - The Feynman Lectures on Physics]
*[https://www.youtube.com/watch?v=44mVZdnR6Yc Meissner Effect (Science from scratch)] Short video from Imperial College London about the Meissner effect and levitating trains of the future.
*[https://web.archive.org/web/20160125175255/http://alfredleitner.com/superconductors.html Introduction to superconductivity] Video about Type 1 Superconductors: ''R'' = 0/Transition temperatures/'''B''' is a state variable/Meissner effect/Energy gap (Giaever)/BCS model.
*[http://hyperphysics.phy-astr.gsu.edu/hbase/solids/meis.html Meissner Effect (Hyperphysics)]
*[https://web.archive.org/web/20140828152921/http://web.ornl.gov/info/reports/m/ornlm3063r1/pt2.html Historical Background of the Meissner Effect]

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